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3 years ago

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Two balls are thrown from a cliff. One is thrown directly up, the other directly down. Both balls have the same initial speed, a

nd both hit the ground below the cliff but at different times. Which ball hits the ground at the greater speed: (a) the ball thrown upward, (b) the ball thrown downward, or (c) both the same

1 answer:

Otrada [13]3 years ago

8 0

Answer:

both the same

Explanation:

When a ball is thrown vertically upwards, it experiences that same acceleration due to gravity as an object thrown directly downwards.

This means that if we ignore the effects of air resistance, and the two balls have the same initial speed, they are expected both expected to hit the ground at the same speed as a result of the principle of conservation of energy.

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ladessa [460]

Answer:

conduction

Explanation:

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3 years ago

Read 2 more answers

A triangular plate with height 6 ft and a base of 7 ft is submerged vertically in water so that the top is 2 ft below the surfac

xenn [34]

Answer:

$62.5\int\limits^6_0 {(\frac{7}{6}y^{2}-\frac{49}{3}y+56) } \, dy = 7875 lb$

Explanation:

For this problem to be easier to calculate, we can represent the triangle as a right triangle whose right angle is located at the origin of a coordinate system. (See picture attached).

With this disposition of the triangle, we can start finding our integral. The hydrostatic force can be set as an integral with the following shape:

$\int\limits^a_b$ γhxdy

we know that γ=62.5 lb/ $ft^{3}$

from the drawing, we can determine the height (or depth under the water) of each differential area is given by:

h=8-y

x can be found by getting the equation of the line, which we'll get by finding the slope of the line and using one of the points to complete the equation:

$m=\frac{y_{2}-y_{1}}{x_{2}-x{1}}$

when substituting the x and y-values given on the graph, we get that the slope is:

$m=\frac{0-6}{7-0}=-\frac{6}{7}$

once we got this slope, we can substitute it in the point-slope form of the equation:

$y_{2}-y_{1}=m(x_{2}-x_{1})$

which yields:

$y-6=-\frac{6}{7}(x-0)$

which simplifies to:

$y-6=-\frac{6}{7}x$

we can now solve this equation for x, so we get that:

$x=-\frac{7}{6}y+7$

with this last equation, we can substitute everything into our integral, so it will now look like this:

$\int\limits^6_0{(62.5)(8-y)(-\frac{7}{6}y+7)}\,dy$

Now that it's all written in terms of y we can now simplify it, so we get:

$62.5\int\limits^6_0 {(\frac{7}{6}y^{2}-\frac{49}{3}y+56)}dy$

we can now proceed and evaluate it.

When using the power rule on each of the terms, we get the integral to be:

$62.5[\frac{7}{18}y^{3}-\frac{49}{6}y^{2}+56y]^{6}_{0}$

By using the fundamental theorem of calculus we get:

$62.5[(\frac{7}{18}(6)^{3}-\frac{49}{6}(6)^{2}+56(6))-(\frac{7}{18}(0)^{3}-\frac{49}{6}(0)^{2}+56(0))]$

When solving we get:

$62.5\int\limits^6_0 {(\frac{7}{6}y^{2}-\frac{49}{3}y+56) } \, dy = 7875 lb$

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3 years ago

2. A student drives 7.8-km trip to school and averages a speed of

Alekssandra [29.7K]

Answer:

<em>The total time is: t=451.22 sec</em>

<em>The average speed is: V=34.57 m/s</em>

Explanation:

<u>Average speed</u>

The average speed is calculated by dividing the total distance traveled by an object (x) by the total time it took it to travel that distance (t).

$\displaystyle V=\frac{x}{t}$

Since the student makes the trip in two parts, we have to calculate the total distance and the total time.

We know the distance to school is 7.8 Km = 7,800 m. The student makes his way home over the same distance, thus the total distance is

x=2*7,800 m=15,600 m

The first trip to school was done at an average speed of v1=32.6 m/s. Knowing the distance and speed, we can calculate the time:

$\displaystyle t1=\frac{x1}{v1}=\frac{7,800}{32.6}=239.26\ sec$

The second trip back home was done at an average speed of v2=36.8 m/s. Let's calculate the second time:

$\displaystyle t2=\frac{x2}{v2}=\frac{7,800}{36.8}=211.96\ sec$

The total time is:

$t=239.26\ sec+211.96\ sec=451.22\ sec$

$\boxed{t=451.22\ sec}$

The average speed is:

$\displaystyle V=\frac{15,600}{451.22}=34.57\ m/s$

$\boxed{\displaystyle V=34.57\ m/s}$

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3 years ago

Type the correct answer in the box. Spell the word correctly.

Veronika [31]

Answer:

Vaccination is the procedure by which a person can be immunized against a disease.

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3 years ago

A baseball bat is 32 inches (81.3 cm) long and has a mass of 0.96 kg. Its center of mass is 22 inches (55.9 cm) from the handle

s344n2d4d5 [400]

Answer:

0.24 kgm²

Explanation:

$L$ = length of the bat = 81.3 cm = 0.813 m

$m$ = mass of the bat = 0.96 kg

$d$ = distance of the center of mass of bat from the axis of rotation = 55.9 cm = 0.559 m

$T$ = Period of oscillation = 1.35 sec

$I$ = moment of inertia of the bat

Period of oscillation is given as

$T = 2\pi \sqrt{\frac{I}{mgd}}$

$1.35 = 2(3.14) \sqrt{\frac{I}{(0.96)(9.8)(0.559)}}$

$I$ = 0.24 kgm²

6 0

3 years ago